An analogue of Schur functions for the plane partitions

Abstract

An attempt is described to extend the notion of Schur functions from Young diagrams to plane partitions. The suggestion is to use the recursion in the partition size, which is easily generalized and deformed. This opens a possibility to obtain Macdonald polynomials by a change of recursion coefficients and taking appropriate limit from three to two dimensions – though details still remain to be worked out.